Kullback-Leibler Divergence, Cost Density-Shaping, Stochastic Optimal Control With Applications to Vibration Suppression

The “k cost cumulant” (kCC) control performs competitively with other structural controllers in protecting buildings from natural disasters. These applications constitute vibration suppression problems involving lightly-damped structures with multiple degrees of freedom. While kCC control has delivered excellent performance in such applications, it gives the designer little direct influence over the shape of the cost’s density. The goal of this work is to present the Minimum Kullback-Leibler Divergence Cost Density-Shaping (MKLD-CDS) control paradigm, which enables the designer to shape the cost’s density according to a pre-specified target mean and variance. This new theory is applied to the first-generation Active Mass Driver (AMD) benchmark problem, where the application of MKLD-CDS with the Statistical Target Selection (STS) design method enables a family of stablizing MKLD-CDS controllers to be computed based on parametric targets. MKLD-CDS controllers are found that exceed the performance of a nominal 2CC controller while not compromising this controller’s robust stability.